# std::atanh, std::atanhf, std::atanhl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float atanh ( float num ); double atanh ( double num ); long double atanh ( long double num ); |  | (until C++23)
/*floating-point-type*/ atanh ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float atanhf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double atanhl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> atanh ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double atanh ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the inverse hyperbolic tangent of num. The library provides overloads of `std::atanh` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::atanh` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the inverse hyperbolic tangent of num (tanh-1
(num), or artanh(num)), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error occurs, ±HUGE_VAL, `±HUGE_VALF`, or `±HUGE_VALL` is returned (with the correct sign).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If the argument is not on the interval `[`-1`,` +1`]`, a range error occurs.

If the argument is ±1, a pole error occurs.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is ±0, it is returned unmodified.
- if the argument is ±1, ±∞ is returned and FE_DIVBYZERO is raised.
- if |num|>1, NaN is returned and FE_INVALID is raised.
- if the argument is NaN, NaN is returned.

### Notes

Although the C standard (to which C++ refers for this function) names this function "arc hyperbolic tangent", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic tangent" (used by POSIX) or "area hyperbolic tangent".

POSIX specifies that in case of underflow, num is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::atanh(num) has the same effect as std::atanh(static_cast<double>(num)).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cfloat>
    #include <cmath>
    #include <cstring>
    #include <iostream>
    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        std::cout << "atanh(0) = " << std::atanh(0) << '\n'
                  << "atanh(-0) = " << std::atanh(-0.0) << '\n'
                  << "atanh(0.9) = " << std::atanh(0.9) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "atanh(-1) = " << std::atanh(-1) << '\n';

        if (errno == ERANGE)
            std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_DIVBYZERO))
            std::cout << "    FE_DIVBYZERO raised\n";
    }

Possible output:

    atanh(0) = 0
    atanh(-0) = -0
    atanh(0.9) = 1.47222
    atanh(-1) = -inf
        errno == ERANGE: Numerical result out of range
        FE_DIVBYZERO raised

### See also

asinhasinhfasinhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)
acoshacoshfacoshl (C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)
tanhtanhftanhl (C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)
atanh(std::complex) (C++11) | computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z}}\)artanh(z)) (function template)
C documentation for atanh

### External links

Weisstein, Eric W. "Inverse Hyperbolic Tangent." From MathWorld — A Wolfram Web Resource.

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